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POST UTME REDEEMERS UNIVERSITY 2025 Mathematics | Objective

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Question 1

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the Pythagorean theorem.

A. 8 cm

Correct B. 12 cm

C. 14 cm

D. 16 cm

Correct Answer: B

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Question 2

A random variable X has a probability distribution given by \[ P(X) = \begin{cases} 0.2 & \text{if } X = 1 \\ 0.3 & \text{if } X = 2 \\ 0.5 & \text{if } X = 3 \end{cases} \]. Find the expected value of X.

Correct A. 1.4

B. 1.7

C. 2.1

D. 2.5

Correct Answer: A

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Question 3

Solve the quadratic equation \[ x^2 + 5x + 6 = 0 \].

A. -2

Correct B. -3

C. -1

D. 4

Correct Answer: B

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Question 4

A histogram of exam scores is given below. What is the mean score?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 5

Find the determinant of the matrix \[ \begin{bmatrix} 2 & 3 & 1 \\ 4 & 1 & 2 \\ 3 & 2 & 1 \end{bmatrix} \].

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 6

Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 2x$ about the x-axis.

Correct A. \frac{4}{3}\pi

B. \frac{2}{3}\pi

C. \frac{1}{3}\pi

D. \frac{1}{2}\pi

Correct Answer: A

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Question 7

A random variable X has a probability distribution given by $P$ X = k $ = \frac{1}{2^k}$ for $k = 1, 2, 3, \dots$. Find the expected value of X.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 8

In the diagram below, $ABCD$ is a trapezium with $AB = 6$ cm and $CD = 8$ cm. If $E$ is the midpoint of $BC$, find the area of the triangle $ADE$.

A. 12

Correct B. 15

C. 18

D. 20

Correct Answer: B

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Question 9

A quadratic equation has roots $\alpha$ and $\beta$ such that $\alpha + \beta = 3$ and $\alpha \beta = 2$. Find the equation of the quadratic.

Correct A. x^2 - 3x + 2 = 0

B. x^2 - 3x - 2 = 0

C. x^2 + 3x + 2 = 0

D. x^2 + 3x - 2 = 0

Correct Answer: A

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Question 10

A histogram of the heights of students in a class is shown below. If the total number of students is 50, find the mean height of the students.

A. 160

B. 170

Correct C. 180

D. 190

Correct Answer: C

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Question 11

Find the area under the curve of $ y = \frac{1}{x^2 + 1} $ from $ x = 0 $ to $ x = 1 $.

Correct A. 0.7854

B. 0.4636

C. 0.5723

D. 0.6931

Correct Answer: A

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Question 12

Solve for ( x ) in the equation $ 2^x + 3^x = 5^x $.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 13

Find the determinant of the matrix $ egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} $.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 14

A sequence is defined by $ a_n = 2n + 1 $. Find the sum of the first 5 terms.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 15

A circle has a radius of 4 cm. Find the area of the circle.

A. 50.24

Correct B. 62.83

C. 78.54

D. 100.53

Correct Answer: B

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Question 16

Find the equation of the line pas\sing through the points (2, 3) and (4, 5) in the coordinate plane.

A. y = 2x - 1

Correct B. y = 2x + 1

C. y = -2x + 1

D. y = -2x - 1

Correct Answer: B

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Question 17

Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.

Correct A. $ -3, -1 $ \cup (1, 3)

B. $ -3, -1 $ \cup (1, 3) \cup (3, 4)

C. $ -3, -1 $ \cup (1, 3) \cup $ -4, -3 $

D. $ -3, -1 $ \cup (1, 3) \cup $ -4, -3 $ \cup (3, 4)

Correct Answer: A

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Question 18

Find the probability that the sum of the numbers on the faces of two fair six-sided dice is 7.

A. \frac{1}{6}

B. \frac{1}{12}

C. \frac{1}{36}

Correct D. \frac{5}{36}

Correct Answer: D

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Question 19

Find the equation of the circle with center (2, 3) and radius 4.

Correct A. $ x - 2 $^2 + $ y - 3 $^2 = 16

B. $ x - 2 $^2 + $ y - 3 $^2 = 25

C. $ x - 2 $^2 + $ y - 3 $^2 = 36

D. $ x - 2 $^2 + $ y - 3 $^2 = 49

Correct Answer: A

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Question 20

Solve the system of equations \begin{align*} x + y &= 4 \ x - y &= 2 \end{align*}.

Correct A. \{(2, 2)\}

B. \{(2, 3)\}

C. \{(3, 1)\}

D. \{(4, 0)\}

Correct Answer: A

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Question 21

Determine the value of $\int_0^\pi \frac{\sin^2 x}{1 + \cos^2 x} dx$.

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{8}

D. \frac{\pi}{16}

Correct Answer: A

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Question 22

Solve the inequality $|x - 2| > 3$.

Correct A. $ -\infty, -1 $ \cup $ 4, \infty $

B. $ -\infty, -1 $ \cup $ 1, \infty $

C. $ -\infty, 1 $ \cup $ 4, \infty $

D. $ -\infty, 1 $ \cup $ 2, \infty $

Correct Answer: A

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Question 23

Find the equation of the line pas\sing through the points $$ -2, 3 $$ and $$ 1, -2 $$.

Correct A. y = -\frac{5}{3}x + \frac{13}{3}

B. y = \frac{5}{3}x - \frac{13}{3}

C. y = -\frac{3}{5}x + \frac{13}{5}

D. y = \frac{3}{5}x - \frac{13}{5}

Correct Answer: A

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Question 24

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

Correct A. \frac{1}{2}

B. \frac{1}{4}

C. \frac{3}{4}

D. \frac{3}{5}

Correct Answer: A

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Question 25

Find the magnitude of the vector $\vec{a} = \langle 3, 4 \rangle$.

A. 5

Correct B. \sqrt{5}

C. \sqrt{10}

D. \sqrt{20}

Correct Answer: B

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